Critical points of the Moser-Trudinger functional on conical singular surfaces, I: compactness

Zhijie Chen, Houwang Li

Let $(\Sigma ,g_1)$ be a compact Riemann surface with conical singularites of angles in $(0,2\pi )$, and $f:\Sigma \to \mathbb{R}$ be a positive smooth function. In this paper, by establishing a…